The win cut the gap between Hamilton and leader Rosberg to four points and came after some were questioning the Briton's mental strength and judgement after he made a silly error in qualifying.
Retired triple champion Jackie Stewart, whose tally of 27 wins Hamilton equalled on Sunday, had said on Saturday that the Mercedes driver was hugely talented but "his head certainly seems to have gone a bit."
Wolff said that was not at all the case.
"I think, different to what the perception is, he is mentally very strong and he could cope well with having had problems," he told reporters.
"One of the examples (in the race) was we had another pitstop which wasn't perfect on the left rear. The first thing he (Hamilton) did, he came on the radio and he said: 'Guys, don't worry. Let's make the next one better'.
"He would have moved himself out of that low (point) anyway. But winning at home, winning in front of such a crowd...that's going to give him a big boost."
Wolff said both his drivers had reacted calmly to the situations they were in on Sunday, in a change from some of the heated pit radio conversations that were heard earlier in the season when they fought wheel to wheel.
"There is no negatively excited emotion. Everything goes very calm. It was the same for Nico. He was facing disaster and retirement and he was very calm and trying to go through the settings.
"It was the same with Lewis, the way he communicates with his engineers is just for me 10 out of 10."
Rosberg, who had led by 29 points, suffered his first retirement of the season at Silverstone.
Hamilton, Wolff said, had been focused before the race after the blow of qualifying, when he aborted his last lap under the assumption that the time could not be improved on - only for Rosberg and others to go quicker.
"We spend a lot of time with each other and...he (Hamilton) has a very stable, mature way of tackling things," said the Austrian.